Solve for $x$ and $y$ by deriving an expression for $x$ from the second equation, and substituting it back into the first equation. $\begin{align*}2x+6y &= -4 \\ 3x-6y &= 6\end{align*}$
Solution: Begin by moving the $y$ -term in the second equation to the right side of the equation. $3x = 6y+6$ Divide both sides by $3$ to isolate $x$ $x = {2y + 2}$ Substitute this expression for $x$ in the first equation. $2({2y + 2}) + 6y = -4$ $4y + 4 + 6y = -4$ Simplify by combining terms, then solve for $y$ $10y + 4 = -4$ $10y = -8$ $y = -\dfrac{4}{5}$ Substitute $-\dfrac{4}{5}$ for $y$ in the top equation. $2x+6( -\dfrac{4}{5}) = -4$ $2x-\dfrac{24}{5} = -4$ $2x = \dfrac{4}{5}$ $x = \dfrac{2}{5}$ The solution is $\enspace x = \dfrac{2}{5}, \enspace y = -\dfrac{4}{5}$.